The growing chaos in Iraq and Syria, where thousands of Western recruits have joined terrorist groups to train and fight, is cultivating a global threat that the United States is "going to be dealing with for the next decade," the head of the House Homeland Security Committee warned today.

"As that threat grows overseas, so too does that threat to the homeland," Rep. Michael McCaul, R-Texas, told a group of counterterrorism officials and reporters attending the Aspen Institute's annual national security forum.

McCaul expressed particular concern over Syria, where "the biggest safe-haven in the world" is fostering a union between expert bomb-makers from Yemen and associates of the al Qaeda affiliate in Syria, the Al Nusrah Front, who are jointly working to develop a new generation of undetectable explosives.

Nearly a month ago, U.S. officials, led by the Transportation Security Administration, boosted security measures at airports overseas amid deepening concerns that Syria-based terrorists could be looking to down a U.S.- or Europe-bound plane, with help from one of the thousands of foreign fighters in the region carrying U.S. and European passports.

"It's the biggest threat to the homeland," McCaul said, noting that many of the foreign fighters in Syria, including more than 100 Americans, have "clean documents, legal travel documents" and "can blend in."

"[Now] you have this combination of technology and manpower coming together," McCaul said.

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PHOTO: Seen in this image is "Abu Dujana al-Amriki," who identifies himself as an alleged al Qaeda fighter from the U.S., but who U.S. officials believe to be part of an Assad regime hoax.

Earlier this year, U.S. officials learned that a particularly extreme "subset" of the Al Nusrah Front and other terrorist groups in Syria was teaming up with elements of the Yemen-based group al Qaeda in the Arabian Peninsula to produce "creative" new designs for bombs that could be smuggled onto airplanes, as one source put it.

Asked by ABC News today why U.S. officials didn't boost security measures at airports sooner -- when some of that intelligence was first detected -- McCaul indicated that at first the government only saw "the link," not more specific information about what the joint effort was producing.

"The threat became more credible and specific over time," he said.

Al Qaeda in the Arabian Peninsula built such innovative devices as the "underwear bomb" that ultimately failed to detonate in a plane over Detroit on Christmas Day 2009, and the group is "still very intent on blowing up airplanes," as McCaul described it.

McCaul praised TSA administrator John Pistole, who was in the audience, for "guarding our airports overseas" and doing "exactly the right thing in protecting American lives."

It's unclear exactly which airports overseas are implementing the expanded security measures, which include requiring U.S.-bound passengers to show that cell phones, laptops and other electronic devices can power-up if they want to carry them onboard.

"TSA overseas is stopping these foreign terrorists from getting into the United States," McCaul added. "They do a great job of keeping them out."

But a number of Americans who went to Syria to fight have made it back into the United States in recent years. Some have been arrested and prosecuted for providing support to a terrorist group, while the FBI tries to "maintain coverage" on those in the United States not currently behind bars, the outgoing head of the National Counterterrorism Center, Matt Olsen, said at the Aspen Institute's forum on Friday.

FBI Director James Comey recently said the government is spending "a tremendous amount of time and effort trying to identify" anyone who's gone to Syria, but "the challenge" is how to not miss anyone.

Over four days at the forum in Aspen, current and former U.S. officials warned of a potential homeland threat from the Islamic State, a brutal terrorist group distanced from al Qaeda that is now wreaking havoc in Iraq and Syria. But many officials suggested the group is currently focused on efforts in the region with only "aspirational" hopes to ultimately attack the West.

In Aspen today, Lisa Monaco, President Obama's homeland security and counterterrorism adviser, said she is worried about the threat from the Islamic State, but "not on the most immediate or imminent level."